Part 2: Accidents in Shipping out the Black Gold -The worst case scenario (Exxon

Question

Part 2: Accidents in Shipping out the Black Gold -The worst case scenario (Exxon Valdez was only a partial spill) The Alaska Pipeline terminates at Valdez on Prince William Sound, where the oil is loaded onto Tankers. The typical Valdez tanker holds 1.2 million barrels of crude oil. Suppose this tanker is ruptured by hitting an iceberg in the quiet bay waters (there is a glacier discharging in the northern part). What is the approximate diameter (NOT radius) of the circular area covered by the final oil spill slick (a deadly layer for plankton, sea otters, birds, etc.). Assume the final thickness is 0.1 mm for the continual slick; and it covers a perfect circle. [Thinning below 0.1 mm causes the slick to break into droplets - see below.] Global Marine Oil Pollution Information Gateway thttp://oils.gpa.unep.org/facts/facts.htm]: "Physical transport: Only ten minutes after a spill of 1 ton of oil, the oil can disperse over a radius of 50 metres, forming a slick 10 millimetres thick. The slick gets thinner (less than one mm) as oil continues to spread, covering an area of up to 12 sq,km. After the slick thins to less than the critical thickness of about 0.1 mm, it disintegrates into separate fragments."

Explanation / Answer

The total volume of crude oil spill = 1.2 million barrel
Now, Volume = A.t, where A is the area and t is the thickness. So to find the area we only need to divide volume by thickness.

But volume is given in barrel and thickness is given in mm. So we shall convert barrel into cubic meter (m^3).

1 barrel = 158.9873 L
1 L = 0.001 m^3
Thus 1 barrel = 158.9873 * 0.001 = 0.1589873 m^3.

So 1.2 million barrel = 1.2*0.1589873 million m^3 = 0.19078476 million m^3 = 0.19078476*10^6 m^3 = 190784.76 m^3.

The thickness of spill = 0.1 mm = 0.1 *10^-3 m.
So area of spill = V/t = 190784.76/0.1*10^-3 = 1907847.6/10^-3 = 1907847600 m^2.

Now area of a circle is given by pi*r^2, where r is it's radius.

So we have pi*r^2 = 1907847600.

So r^2 = 1907847600/pi. Now pi= 3.14159. Thus we have
r^2 = 1907847600/3.14159 = 607287265.366m^2
So r = square root (607287265.366) = 24643.1991707 m

Thus diameter of the spill = 2r = 49286.3983 m = 49.2864 Km

So the diameter of the spill is about 49.2864 Km.

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